SIY9.TXT Calculators and Computers 42 Chapter 9 Calculators and Computers For this chapter you will need: a) A calculator or computer with SIN and COS functions. A Sharp EL-506A scientific calculator is available for $25 plus $5 shipping & handling from CAVE Inc, 1/2 Fast Road, Ritner, KY 42639. 606/376-3137. b) Pencil and paper, c) Graph paper, d) An understanding of how to plot a map by hand. You will not need: a) An assistant, b) Any special mathematical training. It is easier, and far more accurate, to calculate rather than to hand plot a map. But unless you already know how to hand plot, the mathematics will just be so much magic to you. Magic is fine for magicians and economists, but magic allows surveyors' blunders to escape undetected. This fancy math comes with even fancier qualifications. Firstly, you can learn this only after you already know how to plot a map by hand. Secondly, if you have only a small amount of surveying, you will probably find it easier to hand plot than to learn this. Thirdly, if you wait until you have an incentive, it will be a lot easier to learn. To do these calculations, you must have a SIN function on your calculator. These are usually called scientific calculators. I prefer a Sharp EL-506A, which does the calculations with one entry, instead of the double entry needed on most other scientific calculators. It also does all trigonometric, logarithmic, power, and inverse functions, as well as calculating mean and standard deviations. And these do not interfere with its use as a common calculator. $25 from CAVE, Inc. A programmable calculator is nice if you know how to program it. I personally have used a 1980 model Radio Shack BC-4000 programmable calculator made by Texas Instruments. It has eight addressable internal memories and fifty program steps. I can calculate everything that I want to know without writing down any intermediate data. If you use a calculator without addressable memories, then you will have to use paper and pencil for memory. SIY9.TXT Calculators and Computers 43 It's a whole lot easier to learn with the paper and pencil, too. This sort of programmable calculator costs about $40. I have also used an assortment of computers. Those computers which I have programmed and which are still on the market at a reasonable price are: Commodore VIC-20, Radio Shack COCO 2, Radio Shack TRS-80 III, Apple //e, Laser 128 (an Apple //c clone), and an ibm [service mark of the Institute for the Befuddlement of the Masses] PC-XT clone. A computer is easier to use than a programmable calculator, but you can't take it into the field with you to calculate while you survey. Even if you have a laptop computer, I doubt that you would take it into the field. A table of data is needed to record and calculate the station locations. Label a sheet of paper with the following headings: TO FROM COMP TAPE RUN INORTH IEAST SNORTH SEAST Comments The first four columns are the raw data taken from the field. For practice, copy the values from Table 1. RUN is the total distance so far. RUN (of the TO station) is RUN (of the FROM station) plus TAPE. INORTH is the incremental distance north for this shot. INORTH is TAPE times the cosine of COMP. IEAST is the incremental distance east for this shot. IEAST is TAPE times the sine of COMP. SNORTH is the summation distance north of wherever you started. SNORTH (TO) is SNORTH (FROM) plus INORTH. SEAST is the summation distance east of where ever you started. SEAST (TO) is SEAST (FROM) plus IEAST. Be sure to keep your pluses and minuses straight. Negative NORTH is south. Negative EAST is west. Don't blunder. To plot your map, use SNORTH and SEAST to plot the location of each station on a piece of graph paper. Start with a clean sheet of graph paper. Draw a North Arrow. Pick a map scale. You can use any map scale here with no loss of precision. For now, chose the same scale as you used to plot your very first map, 100 feet per inch. Pick a place to start. From point 0, draw a line north. Along this north axis, label the distance every 100 feet. Draw and label the east axis. South and west too. SIY9.TXT Calculators and Computers 44 Plot the location of station 0. SNORTH is 0 units north of where ever you called 0. Put a dot on the north axis at 0. SEAST is 0 units east of where ever you called 0. Move the dot which you just put on the north axis to 0 units east. Sounds kinda silly, but 0 is not a special case. Plot the location of station 1 the same way. SNORTH is 153. Put a dot on the north axis 153 hundredths of an inch north of 0. SEAST is 129. Move the dot (maybe it's easier to leave it and make a new dot?) to 129 hundredths of an inch east. That's the location of station 1. That should be the same place as when you located the station the old way, back in Chapter 1. Now you know how you will check your work while learning all these new things. Plot the rest of the stations from the data of Table 1. If you draw lines between the stations, this map should look just like the one which you plotted on Graph 1. You'll have to decide which method to use. Plotting with the Ranger is quick to learn and the map can be drawn in the field as a blundertrap. The calculator is faster and more accurate, especially on long surveys. You'll know when it becomes easier to use a calculator. If you are using inclination, a lengthier table is needed: TO FROM COMP TAPE INCL HDIST RUN INORTH IEAST IUP SNORTH SEAST SUP To correct the measured distance to a true horizontal distance, multiply the distance times the cosine of the inclination. HDIST is TAPE times the cosine of INCL. IUP is the incremental distance up in this shot. IUP is TAPE multiplied times the sine of INCL. SUP is the summation up (elevation) of the station above the starting station. SUP(TO) is SUP(FROM) plus IUP. Negative UP is down. So now you have SUP. What do you do with it? Unless you are plotting 3-D maze caves on 3-D graph paper, you can probably just ignore it. Write in the elevation as necessary. You can also plot a graph using SUP and SNORTH as the axes. This is called a cross section. You could also plot SUP and SEAST. There is a lot more fancy mathematics which can be done, but I doubt many of you will be interested in even this much. If you have a application for some fancier plotting or surveying, ask for special consultation. I'm especially interested in scientific applications. SIY9.TXT Calculators and Computers 45 For those of you who wish to try this method, here are all of my equations in one place. HDIST = TAPE * COS (INCL) RUN (TO) = RUN (FROM) + TAPE INORTH = HDIST * COS (COMP) IEAST = HDIST * SIN (COMP) IUP = TAPE * SIN (INCL) SNORTH (TO) = SNORTH (FROM) + INORTH SEAST (TO) = SEAST (FROM) + IEAST SUP (TO) = SUP (FROM) + IUP CLOSURE = SQR( [SNORTH {A} - SNORTH {B} ]^ 2 + [SEAST {A} - SEAST {B} ]^ 2) CLOSURE percent = CLOSURE * 100 / RUN The symbol "^" ["carrot"] means exponentiate or power in Applesoft and GW- BASIC. The same as "**" on some other computers and in FORTRAN. The function "^ 2" means to square, to multiply by itself. Hopefully, by now you know that "*" means multiply and "/" means divide. Professional surveyors call north "latitude", and east "departure". They also call a map a "plat". Gotta keep the peons convinced that they are stupid. It is very much easier to blunder with the calculator than with a hand plot. And a computer can lie with a straight face even longer than can a politician. I don't pretend to be able to solve all your problems here. You are welcome to a copy of any of my programs, but I've always found it easier to write my own than to make yours work. I have programs for IBM clone PC/MS-DOS [in GW-BASIC {same as BASICA}], Apple II [in Applesoft], COCO 2 [cassette BASIC], TRS-80 III [disk], Commodore [cassette BASIC], and the Texas Instruments programmable calculator [weird machine code]. Only the Apple II and PC are presently on line and supported, but they all worked while I was using them. The PC program and the Apple II program (to a lesser extent) do a lot of things not covered here. These are calculations which are only practical with a computer. SIY9.TXT Calculators and Computers 46 I am especially interested in scientific applications. If you need any custom programming to make my program fit your computer or your application, I will help. But unless your computer is sitting on my desk, you will have to do most of the work. This compuscript was originally written longhand and then typed to make a master for xerographic copying. Typing was a nightmare, and the revisions were a host of tribulations. Writing on a computer compares with writing on a typewriter, just like writing with a ballpoint pen compares with writing with a goose quill and inkberries. As a special one time offer, I will sell to some lucky fool one Radio Shuck COCO 2 computer, complete with my CAVEMAP surveying program for only $50. Be the first to buy this wonderful piece of technology. I have been told that cartridges [an EPROM in an expensive box] are still available for such activities as Pac-Man [Pac-Person? {Pac-Perchild??}] and Donkey Dong. If it won't work as a babysitter, it still might work as a doorstop. Here is a simple BASIC program which should work on any computer. Try it. It is the program SIY2LINR on my PC disk. 1 D=.01745329:PRINT"Instructions in SIY*.TXT Survey It Yourself: The Poor Man's Guide to Land Surveying (c)1990, DP_BYTER -=>Go forth & exponentiate^<=- « Fast Software CAVE Inc Ritner KY 42639 606/376-3137 Quick. Easy. Inexpensive instruments. No magic. 2 INPUT"Compass ($40)";CO:INPUT"Tape ($28)";TA:SN=SN+TA*COS(CO*D): SE=SE+TA*SIN(CO*D):PRINT"SNORTH =";SN,"SEAST =";SE:GOTO 2 'Do you believe in magic? Y\N This is interpreted BASIC. You need GWBASIC or BASICA or help. 3 'Enter direction (as 0 to 360 degrees) and distance from land description. SNORTH = distance north of beginning station, SEAST = distance east. Plot on graph paper, connect the dots, this is the map, or plat, of the property. This is too easy for a 2-liner. Actually, I can do it with only one line of code. 1 D=.01745329:INPUT"Compass ";CO:INPUT"Tape ";TA:SN=SN+TA*COS(CO*D): SE=SE+TA*SIN(CO*D): PRINT"SNORTH =";SN,"SEAST =";SE:GOTO 1 'DP_BYTER, 1/2 Fast Software, Ritner, KY 42639 606/376-3137